For the home run trot injury, this is answered in rule 5.10, which tells us that if an "accident" happens to the runner, another runner may finish the trot around the bases.
I don't know if an ejection would be such an "accident".
However, the same rule 5.10 says that the umpire shall call time (and the ball is dead), when "an umpire orders a player or any other person removed from the playing field."